New Exotic Minimal Sets from Pseudo-Suspensions of Cantor Systems

Real Coboundaries for Minimal Cantor Systems

In this paper we investigate the role of real-valued coboundaries for classifying of minimal homeomorphisms of the Cantor set. This work follows the work of Giordano, Putnam, and Skau who showed that one can use integer-valued coboundaries to characterize minimal homeomorphisms up to strong orbit equivalence. First, we prove a rigidity result. We show that there is an orbit equivalence between ...

Flow-orbit Equivalence for Minimal Cantor Systems

This paper is about ‡ow-orbit equivalence, a topological analogue of even Kakutani equivalence. In addition to establishing many basic facts about this relation, we characterize the conjugacies of induced systems that can be extended to a ‡ow-orbit equivalence. We also describe the relationship between ‡ow-orbit equivalence and a distortion function of an orbit equivalence. We show that if the ...

Minimal Cantor Systems and Unimodal Maps

New examples of Cantor sets in S that are not C-minimal

Although every Cantor subset of the circle (S) is the minimal set of some homeomorphism of S, not every such set is minimal for a C diffeomorphism of S. In this work, we construct new examples of Cantor sets in S that are not minimal for any C-diffeomorphim of S.

Cantor sets

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...